| Autor: |
Wei-Yan Yu, Xiao-Hong Cao |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Mathematics, Vol 11, Iss 9, p 2208 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2227-7390 |
| DOI: |
10.3390/math11092208 |
| Popis: |
Let H be an infinite-dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. In this paper, we characterized the linear maps ϕ:B(H)→B(H), which are surjective up to compact operators preserving the set of left semi-Weyl operators in both directions. As an application, we proved that ϕ preserves the essential approximate point spectrum if and only if the ideal of all compact operators is invariant under ϕ and the induced map φ on the Calkin algebra is an automorphism. Moreover, we have ind(ϕ(T))=ind(T) if both ϕ(T) and T are Fredholm. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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